The application of IRS for NOMA communication has only recently been noticed by some researchers. In [1]}, the authors proposed a simple IRS-assisted NOMA downlink transmission. At first, they employed  spatial-division multiple-access (SDMA) at the AP to generate orthogonal beams, by using the spacial directions of the nearby users' channels. Then, the IRS-assisted NOMA was used to ensure that additional cell-edge users can also be served on these beams by aligning the cell-edge users effective channels with the predetermined beams.
In [2]}, the performance comparison between NOMA and two types of OMA, namely frequency-division multiple-access (FDMA) and time-division multiple-access (TDMA) was studied in an IRS-aided downlink communication network. The transmit power minimization problem was solved for discrete phase shifters at the IRS. It was shown that TDMA is always more power-efficient than FDMA, but, the power consumption of TDMA compared to NOMA depends upon the target rate and the location of the users. The authors in [3]} investigated the spectral efficiency improvement of NOMA networks by presenting an IRS-aided single-input single-output (SISO) network. To do so, they attempted to enhance the performance of the user with the best channel gain, while all other users depended on the IRS.
The authors in [4]} considered the downlink transmit power minimization problem for the IRS-aided NOMA system. They addressed the resulting intractable non-convex bi-quadratic problem by solving the non-convex quadratic problems alternatively, and to solve the non-convex quadratic problems, they employed a difference-of-convex (DC) programming algorithm.
In [5]}, for the first time, the sum-rate maximization problem was addressed for a MISO IRS-aided NOMA system in the downlink transmission. By using the alternating optimization technique, they designed the passive phase shifts of the IRS and the active AP beamforming vector, alternatively, for two cases of ideal and non-ideal IRS phase shifters. In [6]}, the authors aimed to maximize the sum-rate in the uplink transmission of an IRS-aided NOMA system, and they proposed a semi-definite relaxation (SDR)-based algorithm that reached near-optimal solutions. They showed that the IRS-aided NOMA outperforms the IRS-aided OMA in terms of sum-rate.
The Authors in [7]}, study both uplink and downlink transmission of IRS-aided NOMA and OMA systems. Other papers in the IRS-aided NOMA communication are listed here [8]}, [9]}, [10]}, [11]}, [12]}.
